What is the meaning of “may very well be”?

Solution 1:

The expression is may very well.

(The be is part of the progressive infinitive verb be learning.)

May here refers to possibility. The young man or the coed may be learning..., but they may not be. It has a higher possibility than might.

Using very well with may (be learning) can mean several things. It really depends on the speaker's attitude toward the action and/or the tone of voice. It could mean the action has a lesser, equal or greater possibility of happening than indicated by may alone.

"It may rain" = "It's possible that it will rain".
"It may very well rain" = "It's quite [possible] that it will rain".

(From Word Reference, link in same thread as below).

It could be a concession by the speaker:

It may very well rain today, but I'm going to play tennis anyway.

I concede that there's a good chance that it may rain today, but...

Since the next sentence of your text starts with a but clause, it has this similar concessive meaning.

Lastly, in general terms, it could be used ironically, indicating that the speaker doesn't think it's going to happen:

may very well" is sometimes used cynically, followed by "but", as in "What you say may very well be true, but I'm not convinced". In this case, "very well" is being used somewhat ironically, as the speaker really thinks that what you say is not very likely to be true.

(Word Reference).